61,035 research outputs found
Formal Concept Analysis and Resolution in Algebraic Domains
We relate two formerly independent areas: Formal concept analysis and logic
of domains. We will establish a correspondene between contextual attribute
logic on formal contexts resp. concept lattices and a clausal logic on coherent
algebraic cpos. We show how to identify the notion of formal concept in the
domain theoretic setting. In particular, we show that a special instance of the
resolution rule from the domain logic coincides with the concept closure
operator from formal concept analysis. The results shed light on the use of
contexts and domains for knowledge representation and reasoning purposes.Comment: 14 pages. We have rewritten the old version according to the
suggestions of some referees. The results are the same. The presentation is
completely differen
Reasoning about Action: An Argumentation - Theoretic Approach
We present a uniform non-monotonic solution to the problems of reasoning
about action on the basis of an argumentation-theoretic approach. Our theory is
provably correct relative to a sensible minimisation policy introduced on top
of a temporal propositional logic. Sophisticated problem domains can be
formalised in our framework. As much attention of researchers in the field has
been paid to the traditional and basic problems in reasoning about actions such
as the frame, the qualification and the ramification problems, approaches to
these problems within our formalisation lie at heart of the expositions
presented in this paper
Where Fail-Safe Default Logics Fail
Reiter's original definition of default logic allows for the application of a
default that contradicts a previously applied one. We call failure this
condition. The possibility of generating failures has been in the past
considered as a semantical problem, and variants have been proposed to solve
it. We show that it is instead a computational feature that is needed to encode
some domains into default logic
Embedding Non-Ground Logic Programs into Autoepistemic Logic for Knowledge Base Combination
In the context of the Semantic Web, several approaches to the combination of
ontologies, given in terms of theories of classical first-order logic and rule
bases, have been proposed. They either cast rules into classical logic or limit
the interaction between rules and ontologies. Autoepistemic logic (AEL) is an
attractive formalism which allows to overcome these limitations, by serving as
a uniform host language to embed ontologies and nonmonotonic logic programs
into it. For the latter, so far only the propositional setting has been
considered. In this paper, we present three embeddings of normal and three
embeddings of disjunctive non-ground logic programs under the stable model
semantics into first-order AEL. While the embeddings all correspond with
respect to objective ground atoms, differences arise when considering
non-atomic formulas and combinations with first-order theories. We compare the
embeddings with respect to stable expansions and autoepistemic consequences,
considering the embeddings by themselves, as well as combinations with
classical theories. Our results reveal differences and correspondences of the
embeddings and provide useful guidance in the choice of a particular embedding
for knowledge combination.Comment: 52 pages, submitte
A Logic Programming Approach to Knowledge-State Planning: Semantics and Complexity
We propose a new declarative planning language, called K, which is based on
principles and methods of logic programming. In this language, transitions
between states of knowledge can be described, rather than transitions between
completely described states of the world, which makes the language well-suited
for planning under incomplete knowledge. Furthermore, it enables the use of
default principles in the planning process by supporting negation as failure.
Nonetheless, K also supports the representation of transitions between states
of the world (i.e., states of complete knowledge) as a special case, which
shows that the language is very flexible. As we demonstrate on particular
examples, the use of knowledge states may allow for a natural and compact
problem representation. We then provide a thorough analysis of the
computational complexity of K, and consider different planning problems,
including standard planning and secure planning (also known as conformant
planning) problems. We show that these problems have different complexities
under various restrictions, ranging from NP to NEXPTIME in the propositional
case. Our results form the theoretical basis for the DLV^K system, which
implements the language K on top of the DLV logic programming system.Comment: 48 pages, appeared as a Technical Report at KBS of the Vienna
University of Technology, see http://www.kr.tuwien.ac.at/research/reports
- …